We propose a novel NMF algorithm, named Total Variation constrained Graph-regularized Convex Non-negative Matrix Factorization (TV-GCNMF), to incorporate total variation and graph Laplacian with convex NMF. In this model, the feature details of the data are preserved by a diffusion coefficient based on the gradient information. The graph regularization and convex constraints reveal the intrinsic geometry and structure information of the features; thereby, obtaining sparse and parts-based representations. Furthermore, we give the multiplicative update rules and prove convergence of the proposed algorithm. The results of clustering experiments on multiple datasets, under various noise conditions, show the effectiveness and robustness of the proposed method compared to state-of-the-art clustering methods and other related work.